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How is expected loss determined?

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The quantitative factors and risk components used to determine the expected loss on a credit exposure are probability of default (PD), loss given default (LGD) and exposure at default (EAD).

Expected Loss Formula
EL = PD x LGD x EAD
Where:
EL = Expected loss
PD = Probability of default
LGD = Loss given default
EAD = Exposure at default

Probability of default (PD) represents the risk, expressed as a percentage, that a debtor (borrower, lessee) will default in the coming 12 months, determined by evaluating the debtor’s current and future ability to fulfill its interest and principal repayment obligations.  PD takes into account the characteristic and credit history of the debtor and the nature of the transaction.  It provides a continuous spectrum of default risk and shows how much difference there is in credit quality between credits.  Probability of default is obligor risk – not transaction risk – and is measured separately from the risk of loss or inadequate recovery of asset collateral value.  Internal ratings and the ratings of external ratings agencies may be used to determine PD.

One-Year US Commercial Transition Rates 2014 (%)
Rating at End of Year (%)
Initial AAA AA A BBB BB B CCC/C D NR
AAA 87.03 9.03 0.54 0.05 0.08 0.03 0.05 0.00 3.19
AA 0.54 86.53 8.14 0.54 0.06 0.07 0.02 0.02 4.07
A 0.03 1.83 87.55 5.38 0.35 0.14 0.02 0.07 4.64
BBB 0.01 0.11 3.58 85.44 3.75 0.56 0.13 0.20 6.23
BB 0.01 0.03 0.14 5.16 76.62 6.96 0.66 0.76 9.64
B 0.00 0.03 0.10 0.21 5.40 74.12 4.37 3.88 11.89
CCC/C 0.00 0.00 0.14 0.22 0.65 13.26 43.85 26.38 15.49
Source: Standard & Poor’s

Loss given default (LGD) is the percentage of a defaulted exposure that is expected to be lost and charged off if default occurs, it measuring the loss severity on defaulted obligations and is the reciprocal of the recovery rate (1 - recovery rate).  For equipment leases, the asset’s expected loss is driven by its depreciation curve.  At the time of default, a lease’s LGD is essentially the difference between the exposure at default (EAD) – its unamortized balance (UAB) or net book value (NBV) – and the leased asset’s (exposure’s) fair market value (FMV) at default:

LGD%= EAD - E(FMV)/EAD

The recovery rate (RR) is the percentage of a defaulted financing that a creditor receives in final settlement of its claims on its defaulted claims (lease, loan), it comprising the expected cash flows from the realization of collateral and is the reciprocal of the loss given default (1 - LGD).  The proportion of a defaulted debt that a creditor can recover depends largely on whether it is bank lending, leasing or a marketable instrument (e.g., bond) as well as the type of asset being financed. 

Exposure at default (EAD) is the exposure of a creditor (bank, leasing company) at the moment the debtor goes into default equal to the unamortized balance of a financial exposure (lease, loan) at default.  A leased asset’s unamortized balance (UAB) is the lessor’s net investment in the asset less the amount of accumulated amortization since lease inception, which is the current value of the lease receivable.  Therefore, at any given point during the term of a lease, its expected loss at default is the contract’s probability of default times its loss given default times its unamortized balance:

EL = PD x LGD x UAB

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